Long Division Calculator with Decimals

Long Division with Decimals

Long division with decimals is a key math skill that helps solve real-world problems involving money, measurements, and percentages. Once you learn how to handle the decimal point, dividing decimals becomes as simple as dividing whole numbers. This guide will teach you how to perform long division with decimals step-by-step, with clear examples, formulas, and practice problems.

What Is Long Division with Decimals?

Long division with decimals means dividing numbers that have a decimal point. The process is similar to normal long division, except you must correctly position and move the decimal point.

For example:

Dividend ÷ Divisor = Quotient

In decimal division, either the dividend, divisor, or both may have decimal parts.

Example:

4.8 ÷ 0.2 = 24

To make the division easier, move the decimal point in both numbers so the divisor becomes a whole number.

If this concept feels tricky, tools like the Long Division Calculator can visualize the process instantly.

Steps to Do Long Division with Decimals

Mastering decimal division involves a few clear steps. Let’s go through them one by one.

Step 1 – Set Up the Division Problem

Write the dividend (the number being divided) inside the division symbol and the divisor outside.
Example:

12.6 ÷ 0.3

Step 2 – Move the Decimal Point

To simplify, move the decimal point in the divisor until it becomes a whole number.
If you move it one place to the right, do the same for the dividend.

Example:

12.6 ÷ 0.3 → 126 ÷ 3

Now you can divide normally.

Step 3 – Divide as with Whole Numbers

Ignore the decimals for now.

126 ÷ 3 = 42

Step 4 – Place the Decimal in the Quotient

Count how many places you moved the decimal point in both numbers. The quotient will reflect that movement automatically.

12.6 ÷ 0.3 = 42

Step 5 – Check Your Answer

Always verify by multiplying the quotient by the divisor:

42 × 0.3 = 12.6

If the result matches your dividend, your division is correct.

You can also check answers using the Math Equation Solver.

Examples of Long Division with Decimals

Examples reinforce the concept and help you understand how decimal movement affects the answer.

Example 1 – Dividing a Decimal by a Whole Number

12.6 ÷ 3

Divide as normal:

12 ÷ 3 = 4
6 ÷ 3 = 2
Answer: 4.2

Example 2 – Dividing a Whole Number by a Decimal

24 ÷ 0.6

Move the decimal one place right for both numbers:

240 ÷ 6 = 40

Example 3 – Dividing Two Decimals

0.48 ÷ 0.12

Move the decimals two places right:

48 ÷ 12 = 4

Example 4 – Word Problem Example

You have 3.6 meters of rope and need to cut pieces of 0.3 meters each.

3.6 ÷ 0.3 = 12

You can make 12 equal pieces of rope.

For advanced practice, you can use the Decimal and Integer Calculator for instant results.

Tips to Master Long Division with Decimals

Common Mistakes to Avoid

  1. Not shifting the decimal point properly.
    Forgetting to move the decimal in both numbers leads to incorrect quotients.
  2. Misplacing the decimal in the quotient.
    Always align it directly above its position in the dividend.
  3. Ignoring trailing zeros.
    For example, 3 ÷ 0.5 = 6, not 0.6.
  4. Rounding too early.
    Perform complete division first, then round if needed.

Practice Problems (With Answers)

ProblemAnswer
8.4 ÷ 0.712
0.63 ÷ 0.097
5.25 ÷ 0.1535
7.5 ÷ 0.515
3.6 ÷ 0.312
2.4 ÷ 0.0460

Try verifying these answers using the Mixed Number to Decimal Calculator or the Standard Form Calculator.

Practice Worksheet for Decimal Division

To get better, try these problems on paper or with a calculator.

QuestionHint
1. 4.5 ÷ 0.5Move decimal 1 place right
2. 7.2 ÷ 0.3Estimate: answer should be over 20
3. 0.64 ÷ 0.08Think: 64 ÷ 8
4. 18 ÷ 0.9Simple rounding
5. 25.2 ÷ 0.06Large number expected

You can use the Rounding Numbers Calculator for precise rounding after division.

Real-Life Applications of Decimal Division

Understanding how to divide decimals is vital for solving everyday math problems:

  • Money and Finance: Splitting $12.75 among 3 people → $4.25 each.
  • Cooking and Recipes: Dividing 2.4 liters of juice into 0.3-liter cups → 8 cups.
  • Science and Measurements: Dividing 6.25 grams of a substance into 0.25-gram samples → 25 samples.

For related conversions, check:

For deeper math insights, visit Britannica’s Mathematics Portal — it provides excellent background reading on mathematical concepts without competing for your keyword.

Long Division with Decimals — FAQs

Q1: How do you divide when the divisor is a decimal?
Move the decimal point in both the divisor and dividend until the divisor becomes a whole number. Then divide normally.

Q2: What if both numbers have decimals?
Move the decimal point in both numbers by the same number of places to eliminate the decimal from the divisor.

Q3: How can I check my answer?
Multiply the quotient by the divisor. The product should equal the original dividend.

Q4: Are there tools that handle decimal division automatically?
Yes — try the Long Division Calculator or the Math Equation Solver for step-by-step solutions.

Q5: How is decimal division used in school math?
It forms the foundation for understanding fractions, ratios, and algebraic expressions.

Long division with decimals may look intimidating, but once you understand how to move the decimal point and set up the problem correctly, it becomes second nature.

Remember:

Dividend ÷ Divisor = Quotient

With consistent practice — whether manually or using online tools — you can master decimal division quickly.

To continue building your math skills, explore more interactive tools such as:

By mastering this fundamental operation, you’ll unlock better understanding in algebra, geometry, finance, and science — wherever decimals appear.